A random sample of size 8 – x 1 = 1 , x 2 = 0 , x 3 = 1 , x 4 = 1 , x 5 = 0 , x 6 = 1 , x 7 = 1 , and x 8 = 0 –is taken from the probability function p X ( k ; θ ) = θ k ( 1 − θ ) 1 − k , k = 0 , 1 ; 0 < θ < 1 Find the maximum likelihood estimate for θ .
A random sample of size 8 – x 1 = 1 , x 2 = 0 , x 3 = 1 , x 4 = 1 , x 5 = 0 , x 6 = 1 , x 7 = 1 , and x 8 = 0 –is taken from the probability function p X ( k ; θ ) = θ k ( 1 − θ ) 1 − k , k = 0 , 1 ; 0 < θ < 1 Find the maximum likelihood estimate for θ .
A random sample of size
8
–
x
1
=
1
,
x
2
=
0
,
x
3
=
1
,
x
4
=
1
,
x
5
=
0
,
x
6
=
1
,
x
7
=
1
, and
x
8
=
0
–is taken from the probabilityfunction
p
X
(
k
;
θ
)
=
θ
k
(
1
−
θ
)
1
−
k
,
k
=
0
,
1
;
0
<
θ
<
1
Find the maximum likelihood estimate for
θ
.
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
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Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License